1. Field of the Invention
This invention relates to an f.theta. lens used in a laser scanning optical system or the like, and particularly to an f.theta. lens comprised of a lens and an image forming apparatus using the same.
2. Related Background Art
Heretofore, in a scanning optical system, chiefly a laser source such as a semiconductor laser has been used as a light source and light from the light source has been imaged on a plane to be scanned through an optical system to thereby form a laser spot, and the laser source has been subjected to modulation conforming to image information while the laser spot is scanned on the plane to be scanned by a deflector such as a polygon mirror disposed in the optical path, whereby a desired image has been formed on the plane to be scanned.
Where such a laser scanning optical system is particularly an optical system which scans a laser by the rotation of a deflector such as a polygon mirror, it is desirable that a laser spot be uniformly formed on the whole plane to be scanned (that is, the curvature of image field of a lens system be corrected) and the angle of rotation of the deflector and the position of the spot formed on the plane to be scanned have a proportional relation (that is, the speed of the spot scanned on the plane to be scanned become constant on the whole plane to be scanned, i.e., have constant speed property.). For this purpose, a correcting optical system is used between the polygon mirror and the plane to be scanned. Usually, this lens for correction used in the laser scanning system is a lens called an f.theta. lens having such a distortion characteristic that the angle of incident light and the image height are in a proportional relation, so as to have constant speed property.
Further, even where a mirror surface which is the deflecting surface of the deflector has an inclination, it is regarded as desirable from the viewpoints of the manufacture of the deflector and the quality of image to have optical correcting means so that the position of the scanning line may not deviate (inclination correcting function).
There have been made numerous inventions relating to an f.theta. lens having such inclination correcting function. Particularly, regarding a type in which the number of constituent lenses is two or more, many inventions have been made and put into practical use.
In contrast, several f.theta. lenses in which the lens system is constructed of a lens have also been devised as simpler optical systems.
As seen, for example, in Japanese Laid-Open Patent Application Nos. 55-7727 and 58-5706, there is an example in which an f.theta. lens is comprised of a spherical lens.
Also, like Japanese Laid-Open Patent Application Nos. 63-50812 and 1-224721, there is an example in which a toric surface is used as a lens surface and yet an f.theta. lens is constructed.
Further, in Japanese Laid-Open Patent Application Nos. 54-87540 and 54-98627, there is disclosed an example in which an aspherical surface term is introduced into a single lens, and in Japanese Laid-Open Patent Application Nos. 62-138823, 63-157122 and 2-87109, there is disclosed an example in which a high-order aspherical surface is introduced into a lens surface to thereby construct an f.theta. lens.
However, in the plano-convex f.theta. lens disclosed in Japanese Laid-Open Patent Application No. 55-7727 among the above-mentioned examples of the prior art, constant speed property is corrected, but curvature of image field remains and it is difficult to keep the uniformity of spot. In this case, if design is made such that the size of the effective scanning width by this lens is sufficiently large relative to the plane to be scanned, curvature of image field can be made small, but the entire apparatus will become bulky, and this cannot be said to be practical.
In Japanese Laid-Open Patent Application No. 58-5706, the f.theta. lens comprising a spherical lens is made into a meniscus lens having its concave surface facing the deflecting surface side to thereby accomplish aberration correction, but as in Japanese Laid-Open Patent Application No. 55-7727, an attempt to sufficiently correct curvature of image field and constant speed property at a time would give rise to the necessity of making the distance between this lens and the plane to be scanned great.
In Japanese Laid-Open Patent Application No. 63-50812, a toric lens is used to make a lens in which curvature of image field and constant speed property are corrected. Particularly, the aberrations in the main scanning plane (curvature of image field and constant speed property) and the aberrations in the sub-scanning plane perpendicular to the main scanning plane can be corrected independently and therefore, better correction than in the aforedescribed two examples is accomplished. Further, the deflecting surface and the plane to be scanned are made into a conjugate relation on the sub-scanning cross-section, thereby accomplishing the correction of the inclination of the mirror surface of the deflector as well. The distance from the deflecting surface to the plane to be scanned is also kept relatively small. However, a toric lens, if viewed only in the main scanning plane, is equivalent to a spherical single lens, and it is difficult to correct curvature of image field and constant speed property at a time. Therefore, to provide a lens shape in which aberrations are good, it is necessary to make the thickness t of the lens considerably great relative to the focal length f, i.e., 0.3&lt;t/f&lt;0.5, as described in this patent application. For this reason, as an actual lens, the manufacture thereof is difficult and the use of a single lens will lead to no merit.
In Japanese Laid-Open Patent Application No. 1-224721, a toric lens is also used and further, design is made such that convergent light is caused to enter the toric lens, thereby accomplishing aberration correction, but as in Japanese Laid-Open Patent Application No. 63-50812, even in the main scanning plane alone, it is difficult to make curvature of image field and constant speed property compatible. In this example, as described in the specification thereof, constant speed property is restricted to such a degree of correction that it can be electrically corrected (expressed as substantially constant speed in the specification), whereby the correction of curvature of image field is effected preponderantly. Thus, during image writing, the timing of image information is varied to thereby correct the distortion of the written image. In this case, however, constant speed property is under-corrected and thus, the speed of the spot on the plane to be scanned varies at all times, and the quantity of light received per unit time by the plane to be scanned is varied. It is possible to correct this by varying the quantity of laser light produced from the light source, but this will lead to too many correcting circuits, which does not mean the obtainment of the merit of using a single lens.
In the case of a single lens whose lens shape is a spherical shape in the main scanning plane as in these examples, it has been difficult to realize an f.theta. lens having a sufficient characteristic.
In contrast, as described in Japanese Laid-Open Patent Application Nos. 54-87540 and 54-98627, there is known an example in which an aspherical term is introduced to construct an f.theta. lens.
The aspherical lenses described in Japanese Laid-Open Patent Application Nos. 62-138823, 63-157122 and 1-99013 are such that the shape of the lens near the optical axis thereof is that of a meniscus lens in which the deflecting surface side is a concave surface or a biconvex lens, and in any of these lenses, the thickness t of the lens is great relative to the width of the plane to be scanned.
The example shown in Japanese Laid-Open Patent Application No. 62-138823 is a meniscus lens in which the deflecting surface side is a concave surface or a biconvex lens, but the thickness of the lens is 20 mm at smallest relative to the effective scanning width of 200 mm.
The example shown in Japanese Laid-Open Patent Application No. 63-157122 is a meniscus lens in which near the optical axis, the deflecting surface side is a concave surface, but the thickness of the lens is 30 mm at smallest relative to the maximum scanning width (the scanning width corresponding to the angle of view mentioned as the maximum scanning angle .theta.max in the specification; 254 mm or so in any embodiment).
The example shown in Japanese Laid-Open Patent Application No. 2-87109 is a lens which is biconvex near the optical axis and therefore, the thickness of the lens is also great.
It is difficult to make such aspherical lenses by carrying out the processing as is done in the manufacture of ordinary spherical lenses. Therefore, processing and molding are carried out by the use of materials such as plastics rich in workability to make such aspherical lenses, thereby solving the problem in manufacture. However, plastics are generally apt to be affected by environmental fluctuations, and are particularly apt to be varied in refractive index by humidity and temperature. Especially, where the thickness of the lens is great, a light beam passing therethrough is greatly subjected to a variation in refractive index and thus, the imaging position is varied by environmental fluctuations. Further, a great thickness of the lens is a factor which increases internal homogeneity, distortion, molding termination time, etc. in carrying out processing and molding.
Thus, the aspherical lenses known as the above-described three examples of the prior art could not be said to be practical because of their great lens thicknesses. Particularly in these examples, the shape of the deflection point side lens surface in the main scanning plane is not appropriate and therefore, to satisfy the performance necessary as an f.theta. lens, it is necessary to make the lens thicker than the practical range, and this has been low in realizability.